%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET411-6 : TPTP v9.2.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:07:50 PM UTC 2026
% Result : Unsatisfiable 1.41s 1.76s
% Output : CNFRefutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 37 ( 19 unt; 8 nHn; 24 RR)
% Number of literals : 60 ( 21 equ; 16 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 45 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(subclass_members,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_members) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(unordered_pair_member,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
cnf(regularity1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(ordered_pair,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(prove_compose_condition_for_singleton_membership1_1,negated_conjecture,
member(ordered_pair(x,y),singleton_relation),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_compose_condition_for_singleton_membership1_1) ).
cnf(prove_compose_condition_for_singleton_membership1_2,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_compose_condition_for_singleton_membership1_2) ).
cnf(element_relation2,axiom,
( member(X1,X2)
| ~ member(ordered_pair(X1,X2),element_relation) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',element_relation2) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
cnf(compose_can_define_singleton,axiom,
intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
file('/export/starexec/sandbox/benchmark/Axioms/SET004-1.ax',compose_can_define_singleton) ).
cnf(c_0_11,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_12,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_13,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
unordered_pair_member ).
cnf(c_0_14,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_15,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
( regular(unordered_pair(X1,X2)) = X1
| regular(unordered_pair(X1,X2)) = X2
| unordered_pair(X1,X2) = null_class ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_18,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_19,plain,
( X1 = null_class
| member(regular(X1),universal_class) ),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_20,plain,
( regular(unordered_pair(X1,X1)) = X1
| unordered_pair(X1,X1) = null_class ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_16])]) ).
cnf(c_0_21,negated_conjecture,
member(ordered_pair(x,y),singleton_relation),
prove_compose_condition_for_singleton_membership1_1 ).
cnf(c_0_22,plain,
unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))) = ordered_pair(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_18]) ).
cnf(c_0_23,negated_conjecture,
~ member(x,universal_class),
prove_compose_condition_for_singleton_membership1_2 ).
cnf(c_0_24,plain,
( unordered_pair(X1,X1) = null_class
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,axiom,
( member(X1,X2)
| ~ member(ordered_pair(X1,X2),element_relation) ),
element_relation2 ).
cnf(c_0_26,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_27,axiom,
intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
compose_can_define_singleton ).
cnf(c_0_28,negated_conjecture,
member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),singleton_relation),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,negated_conjecture,
unordered_pair(x,x) = null_class,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,plain,
( member(X1,X2)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),element_relation) ),
inference(rw,[status(thm)],[c_0_25,c_0_22]) ).
cnf(c_0_31,plain,
( member(X1,element_relation)
| ~ member(X1,singleton_relation) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,negated_conjecture,
member(unordered_pair(null_class,unordered_pair(x,unordered_pair(y,y))),singleton_relation),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,negated_conjecture,
( member(x,X1)
| ~ member(unordered_pair(null_class,unordered_pair(x,unordered_pair(X1,X1))),element_relation) ),
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_34,negated_conjecture,
member(unordered_pair(null_class,unordered_pair(x,unordered_pair(y,y))),element_relation),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,negated_conjecture,
member(x,y),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_35]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET411-6 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n002.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:22:01 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.41/1.76 % Version : CSE_E---1.7
% 1.41/1.76 % Problem : theBenchmark.p
% 1.41/1.76 % SZS status Unsatisfiable for theBenchmark.p
% 1.41/1.76 % SZS output start CNFRefutation
% See solution above
% 1.41/1.76 % Total time : 1.372s
%------------------------------------------------------------------------------